What does the notation f(t)1(t) signify?

Question

I've come across this notation in a text on Control Theory, Modern Control Engineering by Katsuhiko Ogata, in a discussion of Laplace transforms. There is little more context I can give than that.

The exact example involves the translation of function $f(t)1(t)$ to $f(t-a)1(t-a)$, so my guess was that it signified some sort of transformation, but I really have no clue.

Google turned up nothing helpful, as did a search on this forum. Any ideas?

Answer 1

$1(t-t_0)$ is simply the step function, also denoted $u(t-t_0)$. $1(t)$ means $u(t-t_0)$ with $t_0=0$.

Its value is $0$ before $t_0$, and $1$ after $t_0$. More info on Wikipedia.

The $1(t)$ is the unit step function and the $f(t)$ is just some other function and when multiplied they can represent some variable signal starting at time $t_0$.

Answer 2

Apparently this is just the author's way of denoting a step function. There doesn't seem to be a reason given for using it.